Self-interaction error induces spurious charge transfer artefacts incore-level simulations of x-ray photoemission and absorption spectroscopyof metal-organic interfaces

Samuel J. Hall, Benedikt P. Klein, and Reinhard J. Maurera)

Department of Chemistry, University of Warwick, Coventry, UK

First principles simulation of x-ray photoemission spectroscopy (XPS) is an important tool in the challeng-ing interpretation and assignment of XPS data of metal-organic interfaces. We investigate the origin of thedisagreement between XPS simulation and experiment for the azulene molecule adsorbed on Ag(111). Wesystematically eliminate possible causes for this discrepancy, including errors in the structural model and finitesize effects in periodic boundary conditions. By analysis of the electronic structure in the ground-state andthe core-hole excited-state, we are able to trace the error back to artificial charge transfer between adsorbedmolecule and metal surface. This is caused by the self-interaction error of common exchange-correlationfunctionals. This error is not remedied by standard hybrid or range-separated hybrid functionals. We employan ad hoc self-interaction error correction based on molecular orbital projection, that exposes this issue andis able to recover the correct experimental behaviour. The charge transfer artefact also negatively affectsthe prediction of X-ray absorption spectra for this system. Both the simulated photoemisson and x-ray ab-sorption spectra show a better agreement with experimental data, once the ad hoc correction is employed.Similar core-hole-induced charge artefacts may affect core-level simulations at metal-organic interfaces moregenerally.

I. Introduction

X-ray photoemission spectroscopy (XPS) plays a cen-tral role in the characterisation of chemical composi-tion, structure, and oxidation state of materials.1,2 It hasproven particularly useful for the analysis and interpre-tation of chemical adsorption at surfaces due to its lowpenetration depth and high surface sensitivity. However,the changes in XP spectra associated with the surface ad-sorption of organic molecules or chemical changes due tosurface reactions are often challenging to interpret whenmultiple chemical environments of the same species arepresent.3

First principles simulation of core level spectroscopyhas proved to be an effective tool to disentangle complexoverlapping XP signatures of hybrid organic-inorganic in-terfaces for both monolayer4 and multilayer thin films.5

Recent example studies where core-level simulation wasvital for the interpretation of experimental spectra in-clude oxygen species on Pt(111),6 and Porphin onAg(111) and Cu(111)7. Klein et al. have shown in aseries of recent joint experimental and computationalstudies how XPS and Near-Edge X-ray Absorption Spec-troscopy (NEXAFS) provide evidence for the differencesin surface chemical bonding between Naphthalene (Nt)and its topological isomer Azulene (Az) adsorbed onAg(111), Cu(111) and Pt(111) surfaces.8–11

Despite these successes in computational simulation ofXP spectra, we may ask: How do we objectively assessif a first principles simulation of a spectrum composedof so many similar signals provides the “right predictionfor the right reason”, i.e. how do we know that it re-produced the spectrum by predicting the correct binding

a)Electronic mail: r.maurer@warwick.ac.uk

energies of each individual atom? This question is noteasily answered for large π-conjugated molecules thatfeature many sp2-hybridised carbon atoms with similarchemical environments. In many cases, the experimentalresolution will not allow us to distinguish features withsubtle chemical shifts and what is present in the experi-mental XP spectrum is a single broad, composite featurethat incorporates most C 1s peaks. In such a scenario,chemical changes due to weak surface adsorption maylead to shifts between individual features, but the over-all XPS signal may appear ultimately unaffected. Equally,errors in core-hole constrained Density Functional The-ory (DFT) simulations of XP spectra may lead to the in-correct ordering of shifts between different carbons, yetthe composite signal may appear to have the right shapeand position. This cannot be resolved without recourseto higher-level theory such as for example Many BodyPerturbation Theory at the GW level,12,13 which is cur-rently computationally intractable to be employed formolecule-metal interfaces.

For most systems, relative binding energy shifts be-tween carbon atoms will be too small to experimentallyresolve them, so this question has mostly academic value.However, naphthalene (Nt) and azulene (Az) adsorbedon Ag(111) and Cu(111) provide interesting cases wherewe can assess simulation accuracy. Both molecules areisomeric bicyclic hydrocarbons with the chemical for-mula of C10H8, but while naphthalene consists of two6-membered rings, azulene possesses one 5-memberedand one 7-membered ring (see inset in Fig. 1a). Thisseemingly small change in structure comes with a changeof topology, leading to drastic differences in electronicstructure, fundamental gap, reactivity, and XP spectro-scopic fingerprint observed in the C 1s spectra.8,14,15

In addition, the difference in topology of those twomolecules leads to significantly different adsorption be-

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haviour on metal surfaces.8–11

In the past, we have created structural models thatagree with experimental structure characterisation andwe have performed XP simulations of naphthalene andazulene that generally agree well with experiment. Thenotable exception here is the case of azulene adsorbedon Ag(111). For this system, the experimental C 1s peakshows a shoulder at low binding energies (similar towhat was observed in the molecular multilayer), yet ourcalculations have shown no evidence of such a shoulder(see Fig. 1d). This represents a clear qualitative disagree-ment between theory and experiment, yet the adsorptionstructure is fully understood.

In this work, we investigate the origin of the disagree-ment between XPS simulation and experiment for azu-lene on Ag(111). We systematically exclude possiblecauses for this discrepancy including errors in the struc-tural model and finite size effects in periodic bound-ary conditions. By analysis of the electronic structurein the ground-state and the core-hole excited state, weare able to trace the error back to artificial charge trans-fer that arises from the self-interaction error of commonexchange-correlation functionals. Crucially, this artifi-cial charge transfer only materialises in the presence ofa core-hole. This error does not appear to be fully reme-died by standard hybrid or range-separated hybrid func-tionals. We employ an ad hoc self-interaction error cor-rection based on molecular orbital projection,16–18 thatexposes this issue and is able to describe the correct ex-perimental behaviour. In addition, the charge transferartefact negatively affects the prediction of NEXAFS spec-tra for this system and the ad hoc correction also succeedsin improving the agreement between simulated and ex-perimental NEXAFS data.

II. Computational Details

For this work, we use periodic slab structures, the op-timisation of which is described in the previous publi-cations, where they were first described.8,9 In brief, thestructures consist of 4-layer (2

√3×2√

3)-R30° metal slabstotalling 48 metal atoms in an hexagonal unit cell witha 30 Å vacuum layer. Structures were optimised with thePBE exchange correlation (xc) functional19 and the D3van der Waals dispersion correction,20–22 with the bot-tom two metal layers frozen to keep them at their bulkoptimised positions, whilst the top two layers and themolecule were allowed to relax.8,9

XPS simulations were carried out using the ∆SCFmethod23–25 with binding energies obtained as the totalenergy difference between a ground-state and core-holeexcited state calculation. Calculations were performedwith periodic unit cell models and cluster model cut-outsfrom the repeating unit cells to leave a single moleculeon the surface.

The plane wave pseudopotential electronic structurecode CASTEP26 was used to perform calculations withthe periodic models. Calculations made use of the PBEfunctional,19 a cut-off energy of 450 eV along with a

6 × 6 × 1 k-grid (Γ-point only for free molecules andfree standing periodic overlayers without a metal sur-face) was used with a total energy per atom conver-gence of at least 1× 10−6 eV/atom. The core-hole waslocalised onto a specific atom through the creation ofa modified version of default on-the-fly generated ultra-soft pseudopotential (PP),27,28 with an electron removedfrom a core-state and the resulting charge compensatedby the introduction of a positive homogeneous back-ground charge.29 XPS binding energies were calculatedfor all individual atoms in the molecule. The total XPspectrum is calculated by broadening and summation ofall atom contributions. To serve as direct reference in theperiodic calculations, an isolated molecule in a vacuumbox to represent the ‘gas-phase’ structure. The size ofthis cube was 20 Å in all directions which has previouslybeen shown to provide a converged result.30

Cluster calculations were performed with the all-electron numeric atomic orbital code FHI-aims.31 Calcu-lations made use of either the force_occupation_projector(FOP) or force_occupation_basis (FOB) keywords to con-strain a core-hole onto a specific atom. Both approachesyield numerically identical results if the core hole cansuccessfully be localised. In some cases, localisation iseasier to achieve with one or the other as previouslydiscussed.30 FOP calculations followed the methodologyset out by Kahk and Lischner32 which involved (i) an ini-tial calculation with an additional 0.1 electron charge onthe chosen atom for 1 s.c.f step in order to break the sym-metry and to localise the core-hole onto the correct atom,and (ii) removal of the extra core charge before runninga full core-hole calculation. Additional core augmenta-tion basis functions were added onto the core-excitedatom to better represent the core-hole whilst a ‘tight-tier2’ basis set was used for the molecule and first metallayer of the cluster with all lower metal layers utilising a‘light-tier1’ basis set. In addition to the PBE functional,19

XPS binding energy were also calculated using the meta-GGAs SCAN33 and TPSS.34

XPS calculation of the azulene on Ag(111) clustercut-out with the HSE06 hybrid functional35 with an ωvalue of 0.11 bohr−1 were carried out in FHI-aims withthe FOB keyword. For the molecule a ‘tight-tier2’ ba-sis set was used and the metal surface was modeledwith an ‘intermediate-tier1’ basis set, the additional coreaugmentation basis functions as proposed by Kahk andLischner32 were applied to all carbon atoms involvedin the structure instead of only to the excited carbon.Both FOP and FOB calculations were performed to anelectronic convergence setting of 1×10−4e/Å3 for theelectron density, 1× 10−2 eV for the KS-eigenvalues and1× 10−6 eV for the total energy. Molecular Orbital pro-jected Density-of-States (MODOS) calculations were per-formed in CASTEP,16 where the molecular orbitals (MOs)of the free standing overlayer of the system (metal ad-sorbed structure with the metal surface removed) areprojected onto the electronic structure of the relaxed fullsystem.

3

All simulated spectra were obtained by combining thecalculated core-electron binding energies with a Pseudo-Voigt broadening scheme.30,36,37 For the XP spectra, afull width half maximum (FWHM) value of 0.7 eV and aGaussian/Lorentzian (G/L) ratio of 70 %/30 % was used.For the NEXAFS spectra, a photon energy dependentbroadening was used based on three energy ranges withdifferent broadening parameters. The first energy rangeuses a FWHM of 0.75 eV and a G/L of 80 %/20 % andends 5 eV above the first peak. The third range starts15 eV higher than the first peak and uses a FWHM valueof 2.0 eV and a G/L ratio of 20 %/80 %. The intermediaterange connects the two other ranges and encompassesa linearly increasing FWHM and linearly changing G/Lratio. For more detailed information about these broad-ening schemes see Ref.30

III. Results

A. Accuracy of C 1s XPS simulations of azulene andnaphthalene metal-organic interfaces

(C) Balsac 4.10 byK. Hermann, FHI

291 289 287 285Binding Energy (eV)

288 286 284 282 291 289 287 285

291 289 287 285Binding Energy (eV)

(a) (b)

(c) (d)

Figure 1. Comparison of experimental and simulated XPS of ad-sorbed azulene (Az) and naphthalene (Nt). (a) Experimentalspectra of adsorbed Az and Nt multilayers8 compared againstgas-phase simulations. (b) Nt adsorbed on Ag(111), (c) Az ad-sorbed on Cu(111), (d) Az adsorbed on Ag(111). Black linesrepresent experimental XP spectra. For the simulations, col-ored sticks represent contributions from single carbon atomsas shown in (a), with the summation included as a broadenedpeak in grey. Experimental data taken from Ref.9

As part of a joint experiment-theory collaborationstudying aromatic molecules adsorbed on metal surfaces,we have recently made heavy use of XPS and NEXAFSsimulations to complement experimental measurements

and to provide additional insight into interaction mecha-nisms. In these previous publications, surface science ex-periments were performed for azulene and naphthalenein the multilayer8 and adsorbed on the (111) surfacesof Copper8–10, Silver9,10, and Platinum11. We found goodagreement of our DFT calculations with the experimentalvalues for adsorption height and energies as measured byx-ray standing wave and temperature programmed des-orption as well as adsorption calorimetry experiments. Inaddition, these publications showed that XPS and NEX-AFS simulations can achieve highly accurate predictionsof experimental spectra.

In particular, DFT simulations were able to shed lightonto the peculiar shape of the C 1s XPS peak of azulene.Even though the azulene molecule contains no hetero-atoms and possesses no functional groups, the C 1s peakstill shows a pronounced shoulder at the low binding en-ergy side, which is a direct result of azulene’s nonalter-nant topology. The nonalternant topology causes an un-equal charge distribution, with electron accumulation onthe 5-membered ring and electron depletion on the 7-membered ring. The result is the large dipole moment(0.8 D) of azulene,38 as well as a chemical shift in theC 1s binding energies, leading to the shoulder in theXPS peak. Our calculations showed, in agreement withearlier simulations39, that the shoulder is indeed causedby the lower binding energy of the negatively chargedcarbon atoms in the 5-membered ring, compared to themore positively charged atoms in the 7-membered ring.(see Fig. 1a).8

One could argue that the experimental spectra wererecorded on a molecular multilayer of the molecule,while our calculations were performed on a theoreti-cal model of the gas-phase molecule. However, theweak interaction between the molecules in the multi-layer only exerts a minor influence on the XPS bind-ing energies, as we could prove in a recent publica-tion, where we performed additional calculations for themolecular crystal.30

Naphthalene, on the other hand, shows a quite narrowpeak, because all carbon atoms have similar C 1s bindingenergies due to its alternant topology and homogeneouscharge distribution. As the direct comparison betweensimulations and experimental data shows (Fig. 1a), theresolution in the measurements for the molecular multi-layers is not good enough to resolve the small differencein chemical shifts between the secondary and tertiarycarbon environments present in naphthalene. However,this small shift is real and can be resolved with high res-olution measurements performed on molecular vapoursin the gas-phase.40

When naphthalene is adsorbed on the Ag(111) sur-face, the XP spectrum changes very little. Both in themeasurements and the simulations, the same narrowpeak remains and no differential chemical shift is intro-duced by the interaction with the surface (Fig. 1b). Thisfinding is in agreement with all other experimental andcomputational data, which points to a weak interaction

4

between surface and molecule and no significant chargetransfer.9,10

For azulene adsorbed on Cu(111), the situation is dif-ferent (Fig. 1c). Here, all carbon atoms suffer a sig-nificant chemical shift, the resulting peak is residing atlower binding energy and possesses a significant asym-metry on the high binding energy side. The asymmetricpeak shape can be explained by energy loss effects ofthe photoelectron, which are only possible in the pres-ence of significant electronic density of states close tothe Fermi energy.41 This energy-loss effect can not be re-produced at our level of theory. However, the calcula-tions show significant relative shifts for all carbon atoms,and the loss of the difference in binding energies, whichis caused by the inhomogeneous electron distribution ofthe gas-phase molecule. Therefore, XPS measurementsand simulations for azulene on Cu(111) are in agree-ment in showing a strong interaction with the surface,which is also supported by all other experimental andtheoretical data.8–10

Thus, for both naphthalene on Ag(111) and azuleneon Cu(111) it can be said that the XPS simulations com-pare well to the experimental XP spectra and fit perfectlyinto a picture of molecule-metal interaction painted byall other data. For azulene adsorbed on Ag(111), thesituation is quite different. Here the experimental C1s spectrum shows a retention of the shoulder whichseems if anything more pronounced, while the DFT sim-ulation shows a significant change in the chemical shiftsand a loss of the shoulder (Fig. 1d). All other experi-mental and computational data points to a weak inter-action between surface and molecule and no significantcharge transfer,9,10 also leading to the expectation thatthe chemical shift of all carbon atoms should not signif-icantly change due to adsorption and the peak shouldershould be retained. In the following, we will investigatethe cause of the missing shoulder in the simulated C 1sXPS data for azulene on Ag(111).

B. The case of the missing XPS shoulder for azulene onAg(111)

Fig. 2a shows the XP spectrum of gas-phase azuleneand 2d the spectrum for the equilibrium structure of azu-lene adsorbed on Ag(111), both including the contribu-tions of all atomic species. All shifts in the adsorbedspecies are much more closely spaced than in the gas-phase and more closely resemble the case of gas-phasenaphthalene rather than azulene. The simulated spec-tra are shifted so that their respective centres of gravityalign. It appears that carbon atom 1, which is locatedat the apex of the 5-membered ring of azulene is leastaffected by the changes whereas all atoms with higherbinding energies (BEs) located at the 7-membered ringare shifted to smaller BEs and lie closer together in theadsorbed case. Simultaneously, carbon atom 2 on the 5-membered ring is shifted to higher BEs. The result is thatall BEs lie within a range of less than 1 eV and the resul-tant XP spectral envelope constitutes a narrow peak. It is

clear that the azulene on Ag(111) slab model predicts astrong change in chemical environment on some carbonatoms, which is not present in the experimental data.

Possible causes for the discrepancy with experimentcan lie in model errors related to structure, electrostat-ics, or electronic structure. In previous works we haveshown that the lateral and vertical adsorption geome-try of the molecule is in excellent agreement with ex-perimental evidence from LEED, STM, AFM, and XSWmeasurements.8,9 We can, therefore, exclude any er-rors in our simulations that stem from misrepresentationof the adsorption structure. It is also known that thechemical shifts are not very sensitive to minor structuralchanges, which we have confirmed with test calculationsfor this system (not shown).

DFT core-hole calculations based on ∆SCF of peri-odic structures are known to be prone to electrostaticartefacts that arise from finite size effects.42 Core-holesare introduced in all periodic repeats of the unit celland if unit cells are not sufficiently large, core-holes canelectrostatically interact with each other, which leads toshifts in the binding energies. These artefacts typicallyconverge relatively quickly with unit cell size and shouldnot be significant in this case.30 Unfortunately, the in-troduction of a homogeneous background charge in pe-riodic core-hole calculations, leads to electrostatic inter-actions that introduce absolute BE shifts that convergeslowly with unit cell size.42,43 However, we have recentlyshown that this typically does not affect relative BE shiftsbetween different species once reasonable unit cell di-mensions are established.30 Kahk et al. have recentlyproposed an approach that remedies these electrostaticeffects and enables the prediction of absolute BEs for pe-riodic structures.44

Fig. 2b shows the simulated spectrum of the free stand-ing overlayer of azulene in the periodicity of the sur-face slab model. The resulting XP spectrum is virtuallyunchanged compared to the gas-phase and correctly ex-hibits a shoulder at low BE. The fact that electrostaticsare not the cause of the discrepancy with experiment isfurther corroborated by our XPS calculations on clustercut-outs of the azulene on Ag(111) structure presentedin Fig. S1 (ESI†). Here we see that, even without theuse of periodic boundary conditions, the C 1s XPS of ad-sorbed azulene lacks a shoulder at low energy.

Having excluded the effects of structure and electro-statics, we turn our attention to the electronic structure.It is reasonable to assume that the misrepresentation ofthe XP spectrum could arise from a misrepresentation ofcharge transfer between molecule and surface. In thetop right corner of Fig. 2, the HOMO and LUMO fron-tier orbitals of azulene are depicted. We can see that theHOMO has more amplitude located at the 5-memberedring, while the LUMO has more probability amplitudelocated on the 7-membered ring. Because the HOMO isoccupied and the LUMO is not, the net charge on the car-bon atoms in the 5-membered ring is negative whereasthe 7-membered ring is partially positively charged, giv-

5

(C) Balsac 4.10 byK. Hermann, FHI

(C) Balsac 4.10 byK. Hermann, FHI

(C) Balsac 4.10 byK. Hermann, FHI

(C) Balsac 4.10 byK. Hermann, FHI

(C) BK. He

(C) Balsac 4.10 byK. Hermann, FHI

HOMO

LUMO

1

2a 3a4a 5a

6

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2 1 0 -1 -2Relative Binding Energy (eV)

2 1 0 -1 -2Relative Binding Energy (eV)

(b)

(c)

(d)

(e)

(f)

(a)

PBE+U(MO)

PBE

Figure 2. DFT simulated XP spectra of azulene in different con-figurations with individual atom shifts shown as coloured lines.All spectra have been shifted to align their respective centres ofgravity. The colours correspond to the highlighted atoms in thestructure shown in the top right corner along with the visuali-sations of the highest occupied molecular orbital (HOMO) andlowest unoccupied molecular orbital (LUMO). (a) Azulene inthe gas-phase, (b) periodic free standing overlayer of Az, (c)Az/Ag(111) with the molecule 12 Å away from the surface,(d) equilibrium geometry of Az/Ag(111). The spectra in (e)and (f) used the same structures as (c) and (d) but include thePBE+U(MO) correction.

ing rise to the substantial dipole moment of the molecule(see Table S1 for net atomic charge and dipole calcu-lations, ESI†). Due to this inhomogeneous charge dis-tribution pattern, charge transfer into the LUMO willlead to more charge being located at the 7-ring and amore homogeneous charge distribution in the anion witha smaller total dipole moment (seen in the calculateddipole moments in Table S1, ESI†), which will affect theBE differences of the carbon atoms. We have performedgas-phase calculations of the XPS spectra of neutral andanionic azulene, which are presented in Fig. S2 (ESI†).As can be seen, the consequence of adding an electronto azulene is that the carbon BEs become more closelyspaced, leading to a narrow XPS signature and to theremoval of the shoulder in the spectrum. We suspectthat the shift of the carbon atoms 1,3,4 and 6, wherethe LUMO is localised, is most responsible for the change

in peak shape. The occupation of the LUMO is likelyalso the cause for the removal of the XPS shoulder in thecase of azulene adsorbed on Cu(111) where significantsurface-molecule charge transfer could be proved.8,9

However, we know from our previous work that thecharge transfer between molecule and surface for azu-lene on Ag(111) as predicted by DFT is very small andonly amounts to 0.01 e as predicted by Bader chargeanalysis.9 Evidence for this is provided by the MO pro-jected DOS for the adsorbed molecule presented inFig. 3a. All occupied gas-phase MOs are located clearlybelow the Fermi level; LUMO and LUMO+1 are fully lo-cated above the Fermi level. Yet, the simulated XP spec-trum is consistent with what we find for a charged gas-phase azulene molecule.

The MODOS in Fig. 3a also shows that the moleculeis only weakly hybridised with the surface as all MO fea-tures are energetically well localised. However, if theissue is due to overly strong chemical interaction and hy-bridisation rather than charge transfer, then a Gedanken-experiment where we lift the molecule from the metalsurface should be able to fully restore the XPS spectrumas predicted by the free standing overlayer shown inFig. 2b. The result for a calculation where the moleculeis 12 Å away from the surface is shown in Fig. 2c and itis puzzling: The XP shoulder at low BE is not restored.While there are some differential shifts within the peaks,they are not of sufficient magnitude to restore the ex-pected peak shape observed in experiment or in the sim-ulated gas-phase or free standing overlayer spectra.

We have established that the simulation error is re-lated to the presence of the surface and consistent withcharge transfer into the molecule, yet no evidence forsuch transfer exists in the ground-state DFT calculationfor the adsorbed or lifted molecule (see Fig. 3a and 3b).We therefore, turn our attention to the core-hole calcu-lations that we use to simulate the BE shifts. To simulatea spectrum for N number of carbon atoms, we performN independent DFT calculations where a 1s core-hole isintroduced for each carbon atom in the molecule. Thepresence of the core-hole leads to orbital relaxation ef-fects and screening of the effective potential that are cap-tured in the total energy that we use to calculate the BEshift. Core-hole relaxation effects can lead to the liftingof orbital degeneracies and orbital realignment that con-tribute to screening or descreening of the relevant carbonatom. As shown in Fig. 3c and 3d where we visualise thecalculated MODOS for azulene on Ag(111) in the pres-ence of the core-hole, the core-hole relaxation effects onthe MODOS of this system are substantial. Most impor-tantly, the LUMO is shifted to lower energies to the pointthat it becomes Fermi level pinned. This is the case forthe adsorbed molecule and the molecule at 12 Å distance,where charge transfer is physically impossible due to thelack of orbital overlap.

In summary, the root cause of the discrepancy be-tween experiment and simulation is therefore an artifi-cial charge transfer between surface and molecule that

6

-4 -2 0 2 4E/EF (eV)

-4 -2 0 2 4E/EF (eV)

Total DOS HOMO-1 HOMO

(a) (b)

(e) (f)

(c) (d)

Azulene/Ag Azulene/Ag 12Å

LUMO LUMO+1

Figure 3. Total density of states and MODOS of structures ofazulene adsorbed on a Ag(111) surface (left) and with the azu-lene molecule 12 Å away from the metal surface (right). (a)and (b) show the results of a ground-state system. (c) and(d) are the core-hole-excited state MODOS. For this plot, theMODOS for all possible core-hole excited carbon species in themolecule have been calculated and summed up. (e) and (f) arethe summed up excited core-hole MODOS with the +U(MO)correction. Total DOS is shown by the black line with grayshading. Occupied orbitals are coloured in blue and unoccu-pied orbitals in red. MO contributions have been scaled for forease of viewing.

arises during the core-hole calculations. The changes ineffective potential as described by the underlying approx-imate xc functional lead to Fermi level pinning even at alarge distance from the surface. This is in contradictionto experimentally measured XP spectra, which are notconsistent with a significant charge transfer into azuleneupon adsorption. In the following, we will apply a cor-rection to our calculations that will demonstrate that thisis actually an artefact of the self-interaction error in thexc description within our DFT calculations.

C. Molecular orbital based self interaction correction:DFT+U(MO)

As can be seen in Fig. 3c and 3d, by removing a core-electron from the C 1s orbital, the effective potential onthe carbon atom becomes more attractive, which reducesthe energy of electronic states with probability on thiscarbon atom. This includes most electronic states. There-fore, the fact that the LUMO orbital of azulene becomesFermi-level-pinned in the core-hole excited state, is likelyrelated to the error in the electron affinity and ionisation

potential, i.e. the underestimation of the HOMO-LUMOgap. This underestimation arises from the many-electronself-interaction error of semi-local xc functionals, suchas the here employed PBE functional. To explore thispoint, we artificially adjust the gap between the HOMOand LUMO state of the azulene molecule with a penaltyfunctional that we add to PBE. We call this approachPBE+U(MO) as it is similar to the use of atomic-orbital-based self-interaction corrections in +U methods,45–48

but the projector states target gas-phase MOs. This ap-proach has previously been implemented in the CASTEPcode.17,18

The DFT+U(MO) energy functional17 is augmentedwith an additional penalty term that leads to an orbital-dependent potential that increases or reduces the energyof the MO under consideration:

V̂c =Uc

2|φc〉 〈φc| (1)

In equation 1, φc refers to the wave function of thereference MO that is to be constrained. The potential isapplied in each step of the self-consistent-field algorithmand leads to the variational optimisation of the Kohn-Sham orbitals under this constraint. The choice of Uvalues for each constrained MO, c, is ad hoc and needsto be manually provided. In our calculation, we applya constraint to the HOMO, the LUMO, and LUMO+1 or-bitals. We identify the values of U for the PBE+U(MO)calculation by searching the space of possible U valuesthat best match the HOMO-LUMO gap predicted by thePBE0 functional49 for the gas-phase azulene molecule ina supercell box. As shown in Table I, we can matchthe HOMO-LUMO gap of the PBE0 functional with thePBE approach with a choice of UHOMO = +2.00 eV,ULUMO = +5.25 eV, and ULUMO+1 = +5.30 eV. Sev-eral combinations of parameters have been explored in-cluding choices with and without application of a con-straint to the LUMO+1 orbital. In cases where we donot constrain the LUMO+1, the orbital ordering is af-fected and the LUMO+1 becomes Fermi level pinned.The same was applied for the gasphase naphthalenemolecule for the data presented in the ESI† where thevalues were UHOMO = +2.00 eV, ULUMO = +5.50 eV,and ULUMO+1 = +5.55 eV.

We test the validity of the PBE+U(MO) approach byfirst applying it to the molecule at 12 Å distance fromthe metal surface shown in Fig. 2e. The method indeedpredicts the correct shape of the XPS in agreement withexperiment. The individual carbon BEs and their rela-tive shifts are in fair agreement with what is found forthe case of the free standing overlayer shown in Fig. 2b.Some of the shifts deviate, particularly the relative BEshift between carbon 1 and 2 in the 5-membered ring.This may be related to the fact that the +U(MO) correc-tion does not fully remove the artificial charge transferinto the molecule for this geometry, as can be seen in theMODOS for the core-hole excited state calculated with

7

Table I. DFT calculated gap between the HOMO and LUMO ofan azulene molecule in a 20 Å periodic vacuum cube performedwith either the PBE0 or PBE exchange correlation functional.PBE+U(MO) value is from a calculation where the positions ofthe HOMO and LUMO and LUMO+1 were shifted by +2.00,+5.25 and +5.30 eV, respectivelyxc Functional HOMO-LUMO Gap (eV)PBE0 3.60HSE06 2.84PBE 2.07PBE+U(MO) 3.60

PBE+U(MO) shown in Fig. 3f. This goes to show thateven orbital energies equivalent to the hybrid functionallevel with PBE0 may not be fully sufficient to remove allartefacts.

In Fig. 2f, we show the PBE+U(MO) XP spectrum forthe metal-adsorbed geometry, which is in good agree-ment with the experimentally measured spectra for themonolayer and the multilayer of azulene adsorbed atAg(111). Particularly noteworthy is the fact that the in-dividual ordering of the carbon atoms in terms of theirBE is fully preserved upon adsorption of the molecule.This is not unexpected as the molecule is only weaklyhybridised and adsorbs in a physisorbed state at about3.1 Å from the metal surface.9

This is the same scenario as for naphthalene onAg(111), where the multilayer, monolayer, and gas-phase XP spectra of the molecule are virtually identi-cal. We note that the spectral prediction for naphtha-lene on Ag(111) may also suffer from errors associatedwith the xc approximation, but similarity between theBEs of all the carbon atoms makes it impossible to usethe experiment as meaningful benchmark reference. Infact, naphthalene on Ag(111) suffers from the same ar-tificial charge transfer issue as azulene as can be seenin Fig. S3b (ESI†). But this issue does not measurablymaterialise, because due to the homogeneous electronicstructure of naphthalene, the charge transfer shifts thecontributions of all atoms equally and does not introducea relative shift as can be seen on in Figure S5 (ESI†). InFig. S3c and S4 (ESI†) we compare the results of thePBE+U(MO) approach for the naphthalene on Ag(111)XP spectrum with the regular PBE result and find that thetotal convoluted spectra are virtually indistinguishable.In contrast, the artificial charge transfer into azulene pre-dominantly affects the shifts of the carbons where theLUMO has significant probability amplitude (see FigureS5, ESI†), which changes the shape of the spectrum.

We further stress that this approach is not a universalsolution to charge transfer artefacts that can arise fromself-interaction error, but rather an ad hoc correction toexemplify the problem. The penalty potential appliedto MO gas-phase reference orbitals is also only reason-able in cases where the MO gas-phase orbitals remainmeaningful representations of the electronic structure,so where the molecule is only weakly hybridised with

the surface.Lasting solutions to this artefact require either the

use of better exchange correlation functionals with non-local exchange and correlation description or the useof excited-state methodology beyond simple ∆SCF-basedcore-hole constraints. We note that even the use ofrange-separated hybrids such as HSE0635 does not rem-edy the shoulder problem for the cluster cut-out we stud-ied in Fig. S1 (ESI†), however, the HOMO-LUMO gappredicted by HSE06 is also considerably lower than thatof PBE0. Unfortunately, bare hybrid xc functionals suchas PBE0 cannot simply be applied to the study of met-als as they do not provide a reliable prediction of themetal electronic structure, but optimally tuned range-separated hybrid functionals with custom optimised pa-rameters for individual systems may be able to addressthe problem.50,51

D. Implications of charge transfer artefacts for NEXAFSpredictions

298296294292290288286284282Photon Energy (eV)

Experiment

(a)

(b)

(c)

simulated withPBE+U(MO) XPS onset

simulated withPBE XPS onset

Figure 4. Comparison of the experimentally measured and sim-ulated NEXAFS data for azulene/Ag(111). (a) experimentalNEXAFS spectrum. (b) and (c) show NEXAFS simulations us-ing the ∆IP-TP method with two different onset corrections tosum up the spectra. (b) uses the XPS binding energies obtainedfrom a ∆SCF calculation with PBE and (c) from a ∆SCF cal-culation with PBE+U(MO). The simulated spectra have beenshifted to align with the experimental energy scale. For bothexperimental and simulated data, a 25◦ incidence angle waschosen. Experimental data taken from Ref.9.

The role of xc errors and the resultant charge transferartefacts in XPS simulation of metal-organic interfacesis a cautionary tale as this can lead to the misinterpre-tation of spectra and wrong conclusions on the surfacechemistry. However, this error can also further affect the

8

simulation of K-edge NEXAFS spectra at metal-organicinterfaces, which are highly valuable for the interpreta-tion of the surface-adsorption-induced changes in elec-tronic structure and also the molecular orientation at thesurface.52,53

While the most common approach to XPS simulationsat the DFT level is the use of ∆SCF in combinationwith the maximum overlap method,54 x-ray absorptionis commonly simulated with the transition potential (TP)method55 based on Slater’s transition state approach.56

We have recently discussed this approach and its techni-cal and numerical aspects in detail.30 In its realisation inperiodic plane wave codes, the core-hole relaxation ef-fects on the valence electronic states are simulated viathe introduction of a half core-hole and a single transi-tion potential calculation of the Kohn-Sham eigenvalues.As the atomic nucleus is represented by a pseudopoten-tial in this approach, the ionisation potential associatedwith the removal of an electron from the 1s state is thencorrected by shifting the spectrum with respect to theBE of the 1s state of the relevant carbon atom calcu-lated with the ∆SCF method, we call this approach ∆IP-TP.29,30 Therefore, prediction errors in the XPS propagateinto errors in the NEXAFS predictions as changes in rela-tive BE shifts will lead to the misalignment of excitationsthat arise from different core-states into the same valencestates.

In Fig. 4 we show the experimentally measured K-edge NEXAFS spectrum of azulene adsorbed on Ag(111)9

against the ∆IP-TP prediction corrected by PBE XPS on-sets (in Fig. 4b) and PBE+U(MO) onsets (in Fig. 4c).We can see that the first resonance of the NEXAFS spec-trum based on the U-corrected XPS energies becomesnarrower and the broad shoulder present at about 285 eVin the PBE-only prediction is reduced. Note that we usethe conventional PBE functional for the TP calculationsof the valence state relaxation and not the +U(MO) ap-proach, because the orbital ordering and spacing of theunoccupied states will likely be affected by the +U(MO)correction. This is due to the fact that we have only se-lected U values under the criterion to reproduce the PBE0HOMO-LUMO gap, but not to correctly capture the opti-cal 1s→LUMO+X excitations of the system.

IV. Conclusion

When calculating core-level spectra for metal-organichybrid interfaces it is important to take into consider-ation various errors that can affect both the absolutebinding energies and relative shifts. Binding energiesare difficult to predict on an absolute energy scale with∆SCF and conventional exchange-correlation approxi-mations in DFT. However, relative shifts between indi-vidual atoms are often less influenced by intrinsic DFT er-rors. In most cases, when studying organic molecules ad-sorbed at surfaces, the overall shape of the spectrum cantherefore be predicted accurately. This does not hold truefor azulene on Ag(111), where spurious charge transferbetween the metal and the molecule is introduced by the

presence of the core-hole. As a consequence, the relativeshifts between the C 1s binding energies of the differ-ent carbon atoms are changed and the predicted shapeof the XP spectrum is too narrow and lacks a shoulderthat is present in the experiment. The problem is seenacross different DFT software packages and occurs forGGA, meta-GGA, and range separated hybrid function-als, both in periodic and aperiodic simulations.

While this artificial charge transfer is likely present inmany molecule-metal interface calculations and we alsofind it to be present in our simulations for naphthaleneon Ag(111), only azulene on Ag(111) seems to be par-ticularly sensitive to this effect. The shoulder in the C 1sXPS of azulene originally arises from the non-alternanttopology of the molecule which leads to an inhomoge-nous charge distribution, which result in unusually largerelative binding energy shifts within a π-conjugated or-ganic molecule. The spurious charge transfer into themolecule that is caused by the core-hole screening andthe underestimation of the HOMO-LUMO gap leads to amore homogeneous charge distribution in the molecule,which also leads to smaller shifts in binding energies ofdifferent carbon atoms. The spurious charge transfer isultimately caused by DFT self-interaction error and weshow that it can be addressed by applying a penalty func-tional method, DFT+U(MO), to either increase or de-crease the energy of unoccupied and occupied molecularorbital states. By applying this ad hoc correction we areable to predict the correct shape of the XP spectrum ofazulene on Ag(111) and furthermore also improve theprediction of the NEXAFS spectrum.

Artificial charge transfer caused by core-hole screen-ing is likely to be common in the simulated core-levelspectra of metal-organic interfaces, but more often thannot it will be invisible as the experimental resolutionof individual carbon shifts will be insufficient. Systemssimilar to azulene with inhomogeneous charge distri-butions may be more strongly affected by this problemand caution is advised when performing and interpretingcore-level simulations in these cases. Potentially prob-lematic systems include molecules with intramolecularcharge-transfer and low-lying conduction states, such asdonor-acceptor polymers or polythiophenes which arecommonly used in organic electronics devices. WhileMany Body Perturbation Theory remains out of reachfor large-scale metal-organic interface models, improvedexchange-correlation functionals will be required to ad-dress the cause of this problem. Due to the difficultyof addressing metallic systems with hybrid functionals,currently only optimally tuned range separated hybridfunctionals may be able to address this problem.50,51

Acknowledgements

This work was funded by the UKRI Future LeadersFellowship programme (MR/S016023/1), the Walter-Benjamin programme of the Deutsche Forschungsge-meinschaft (DFG, KL 3430/1-1), and the EPSRC-fundedCentre for Doctoral Training in Molecular Analytical

9

Sciences (MAS CDT, EP/L015307/1). We acknowl-edge computational resources provided by the ScientificComputing Research Technology Platform of the Uni-versity of Warwick, the EPSRC-funded HPC Midlands+computing centre (EP/P020232/1) and on ARCHER2(https://www.archer2.ac.uk/) via the Materials Chem-istry Consortium (EP/R029431/1).

Competing Interests

The authors declare no competing interests.

Data Availability

The input and output files of the electronic structurecalculations reported in this work have been depositedto the NOMAD repository and can be accessed here: DOIwill be included upon acceptance by publisher.

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Supporting InformationSelf-interaction error induces spurious charge transfer artefacts in

core-level simulations of x-ray photoemission and absorptionspectroscopy of metal-organic interfaces

Samuel J. Halla,b, Benedikt P. Kleina,c and Reinhard J. Maurera

a Department of Chemistry, University of Warwick, Gibbet Hill Rd, Coventry, CV4 7AL, United Kingdom

b MAS CDT, Senate House, University of Warwick, Gibbet Hill Rd, Coventry, CV4 7AL, United Kingdom

c Diamond Light Source, Harwell Science and Innovation Campus, Didcot, OX11 0DE, United Kingdom

S1

arX

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112.

0087

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[co

nd-m

at.m

trl-

sci]

1 D

ec 2

021

(C) Balsac 4.10 byK. Hermann, FHI

2 1 0 -1 -2

Relative Binding Energy (eV)

HSE06 SCAN TPSS PBE

Figure S1: Simulated XP spectra, calculated using the ∆SCF method, of azulene on Ag(111) using anaperiodic cluster structure shown alongside. Calculations were performed using the all-electron DFTsoftware package FHI-aims for three different exchange correlation functionals, HSE06 shown in purple,SCAN in green and TPSS in yellow. HSE06 was calculated using the force_occupation_basis keywordto constrain the core-hole whilst SCAN and TPSS utilised the force_occupation_projector keyword. Allspectra are aligned to the average shift of the individual atoms.

S2

Table S1: Mulliken and Hirshfeld charges and dipole moments calculated for gas-phase azulene usingFHI-aims. Shown are the joint partial charges of the carbon and hydrogen atoms for each symmetryinequivalent CH group. All charges are in units of e, the dipole moments are in Debye.

Carbon 1 2 3 4 5 6 Sum Dipole Moment

Mulliken Neutral 0.00 −0.12 0.10 0.01 −0.02 0.02 0.00 1.03Anion −0.15 −0.31 0.07 −0.28 −0.18 −0.14 −0.01 0.82

Hirshfeld Neutral 0.00 −0.07 0.00 0.06 −0.02 −0.02 −1.00 0.85Anion −0.14 −0.23 −0.10 −0.18 −0.18 −0.13 −0.96 0.67

2 1 0 -1 -2Relative Binding Energy (eV)

(a) Neutral

(b) Anion

Figure S2: DFT simulated XPS of azulene in a gasphase aperiodic structure, performed with the all-electron software package FHI-aims with the indivdual atom shifts shown as coloured lines according tothe labelled structure. Spectra are calculated using the ∆SCF method with (a) keeping the moleculeoverall charge neutral or (b) with the molecule left in an anionic state. Spectra have been aligned to theaverage shift of the individual atom shifts.

S3

-4 -2 0 2 4E/EF (eV)

Total DOS HOMO-1 HOMO

LUMO LUMO+1

(a)

(b)

(c)

Figure S3: Total density of states and MODOS of naphthalene on Ag(111). (a) shows the DOS in theground state, (b) in the core-hole excited state with all individual orbitals summed up and (c) the core-hole excited state with the DFT+U(MO) correction applied. Total DOS is shown by the black line withgray shading. Occupied orbitals are coloured in blue and unoccupied orbitals are coloured in red. Orbitalcontributions have been scaled for ease of viewing.

S4

2 1 0 -1 -2Relative Binding Energy (eV)

PBEPBE+U(MO)

(C) Balsac 4.10 byK. Hermann, FHI

Figure S4: DFT Simulated XP spectra of naphthalene on Ag(111) performed in periodic boundary con-ditions using the CASTEP code using the ∆SCF method (blue) and with the PBE+U(MO) (orange) toshift specific orbitals. Spectra are aligned to the average shift of the individual atoms.

S5

291.8

291.6

291.4

291.2

291.0

290.8

290.6

290.4

290.2

Bin

ding

Ene

rgy

(eV

)

1 2a 2b 3a 3b 4a 4b 5a 5b 6

Carbon

1a 1b 1c 1d 2a 2b 2c 2d 3a 3b

Carbon

PBE PBE+U(MO)

Azulene/Ag(111) Naphthalene/Ag(111)

Figure S5: Absolute carbon shifts for each individual carbon atom in azulene (left) and naphthalene (right)adsorbed onto an Ag(111) surface. Squares represent results from a ∆SCF calculation with CASTEP usingthe PBE functional and circles are results where the PBE+U(MO) correction has been applied.

S6